A spherical Radon transform whose integral domain is a sphere has many applications in partial differential equations as well as tomography.
This paper is devoted to the spherical Radon transform which assigns to a given function its integrals over the set of spheres passing through the origin.
We present a relation between this spherical Radon transform and the regular Radon transform, and we provide a new inversion formula for the spherical Radon transform using this relation.
Numerical simulations were performed to demonstrate the suggested algorithm in dimension 2.

References:

A. M. Cormack, Representation of a function by its line integrals, with some radiological applications,, \emph{Journal of Applied Physics}, 34 (1963), 2722.
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[3]

A. M. Cormack, Representation of a function by its line integrals, with some radiological applications. II,, \emph{Journal of Applied Physics}, 35 (1964), 2908.
Google Scholar

[4]

A. M. Cormack and E. T. Quinto, A Radon transform on spheres through the origin in $\mathbbR^n$ and applications to the Darboux equation,, \emph{Transactions of the American Mathematical Society}, 260 (1980), 575.
doi: 10.2307/1998023.Google Scholar

S. J. Norton, Reconstruction of a reflectivity field from line integrals over circular paths,, \emph{The Journal of the Acoustical Society of America}, 67 (1980), 853.
doi: 10.1121/1.384168.Google Scholar

References:

A. M. Cormack, Representation of a function by its line integrals, with some radiological applications,, \emph{Journal of Applied Physics}, 34 (1963), 2722.
Google Scholar

[3]

A. M. Cormack, Representation of a function by its line integrals, with some radiological applications. II,, \emph{Journal of Applied Physics}, 35 (1964), 2908.
Google Scholar

[4]

A. M. Cormack and E. T. Quinto, A Radon transform on spheres through the origin in $\mathbbR^n$ and applications to the Darboux equation,, \emph{Transactions of the American Mathematical Society}, 260 (1980), 575.
doi: 10.2307/1998023.Google Scholar

S. J. Norton, Reconstruction of a reflectivity field from line integrals over circular paths,, \emph{The Journal of the Acoustical Society of America}, 67 (1980), 853.
doi: 10.1121/1.384168.Google Scholar